1640s, as a theological term (in reference to "covenants" between God and man), from French fédéral, an adjective formed from Latin foedus (genitive foederis) "covenant, league, treaty, alliance" (from PIE *bhoid-es-, suffixed form of root *bheidh- "to trust, confide, persuade").

Secular meaning "pertaining to a covenant or treaty" (1650s) led to political sense of "formed by agreement among independent states" (1707), from use of the word in federal union "union based on a treaty" (popularized during formation of U.S.A. 1776-1787) and like phrases. Also from this period in U.S. history comes the sense "favoring the central government" (1788) and the especial use of the word (as opposed to confederate) to mean a state in which the federal authority is independent of the component parts within its legitimate sphere of action. Used from 1861 in reference to the Northern forces in the American Civil War.

1650s, "active operation;" 1670s, "a mode of exerting power or producing effect," from Medieval Latin agentia, abstract noun from Latin agentem (nominative agens) "effective, powerful," present participle of agere "to set in motion, drive forward; to do, perform," figuratively "incite to action; keep in movement" (from PIE root *ag- "to drive, draw out or forth, move"). The meaning "establishment where business is done for another" is recorded by 1861.

initialism (acronym) for Environmental Protection Agency, U.S. federal agency proposed by President Richard Nixon and created in December 1970.

also I.R.S., initialism (acronym) of Internal Revenue Service, U.S. federal government tax collection agency, attested by 1954. The office dates to 1862; name changed 1953 from Bureau of Internal Revenue.

U.S. Federal Communications Commission, formed 1934 from the former Federal Radio Commission.

1788, "doctrine of federal union in government," American English, from French fédéralisme, from fédéral (see federal). Also, from about the same time and place, "doctrines of the Federalist Party in American politics."

"pertaining to an agent or to an agency," 1847, from Medieval Latin agentia (see agency) + -al (1). Related: Agentially.

U.S. civilian espionage agency, initialism (acronym) of Central Intelligence Agency, founded 1947 as successor to the Office of Strategic Services (OSS).

official news agency of the former U.S.S.R., formed in 1925, an acronym of Russian T'el'egrafnoye ag'enstvo Sov'etskovo Soyuza  "Telegraphic Agency of the Soviet Union."

1787, American English, "member or supporter of the Federal party in U.S. politics" (originally of supporters of the Philadelphia constitution), from federal + -ist. General sense of "one who supports federal union" is from 1792. The party expired c. 1824. As an adjective by 1801.